Cremona's table of elliptic curves

5200 = 2⁴ · 5² · 13

Field	Data	Notes
Atkin-Lehner	2- 5+ 13-	Signs for the Atkin-Lehner involutions
Class	5200w	Isogeny class
Conductor	5200	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	520000000000 = 212 · 510 · 13	Discriminant
Eigenvalues	2-  1 5+  2 -2 13- -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-203333,35222963]	[a1,a2,a3,a4,a6]
Generators	[32470:697:125]	Generators of the group modulo torsion
j	23242854400/13	j-invariant
L	4.5718121794283	L(r)(E,1)/r!
Ω	0.76231612512862	Real period
R	5.9972654765199	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	325e2 20800ck2 46800dw2 5200bf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5200w2

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	1	+	2	-2	-	-2	0	-9	5	-2	8	12	1	-8	-11	0	-13	2	-12	-6	-15	-4	-10	8

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Quadratic twists for elliptic curve 5200w2

-4	8	-3	5	13
325e2	20800ck2	46800dw2	5200bf1	67600bq2

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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